text: For fluids with high molecular complexity, state-of-the-art thermodynamic models predict values of  in the single-phase region close to the saturation curve, where the speed of sound is largely sensitive to density variations along isentropes. Such fluids belong to different classes of chemical compounds, including hydrocarbons, siloxanes and refrigerants.
  In the non-ideal regime, even qualitative differences with respect to ideal gasdynamics can be found, meaning that the flow evolution can be strongly different for varying total conditions. The most peculiar phenomenon of the non-ideal regime is the decrease of the Mach number in isentropic expansions occurring in the supersonic regime, namely processes in which the fluid density decreases. Indeed, for an ideal gas expanding isentropically in a converging-diverging nozzle, the Mach number increases monotonically as the density decreases. By contrast, for flows evolving in the non-ideal regime, a non-monotone Mach number evolution is possible in the divergent section, whereas the density reduction remains monotonic (see figure in the lead section). This particular phenomenon is governed by the quantity , which is a non-dimensional measure of the Mach number derivative with respect to density in isentropic processes: 
  where
  *  is the Mach number;
  *  is the density [kg/m].
  From the definition of , the Mach number increases with density for flow conditions featuring values of . Indeed, this is possible only for values of , that is in the non-ideal regime. However, this is not a sufficient condition for the non-monotone Mach number to appear, since a sufficiently large value of  is also required. In particular, supersonic conditions () are necessary.
  An analogous effect is encountered in the expansion around rarefactive ramps: for suitable thermodynamic conditions, the Mach number downstream of the ramp can be lower than the one upstream. By contrast, in oblique shock waves, the post-shock Mach number can be larger than the pre-shock one.